Inverse matrix gamma distribution

In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices. It is a more general version of the inverse Wishart distribution, and is used similarly, e.g. as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal distribution. The compound distribution resulting from compounding a matrix normal with an inverse matrix gamma prior over the covariance matrix is a generalized matrix t-distribution.

This reduces to the inverse Wishart distribution with ${\displaystyle \nu }$degrees of freedom when ${\displaystyle \beta =2,\alpha ={\frac {\nu }{2}}}$.

• inverse Wishart distribution.
• matrix gamma distribution.
• matrix normal distribution.
• matrix t-distribution.
• Wishart distribution.